Related papers: A Comparative Study for the Evolution of Structure…
We give an outline of a formalism for the solution of the evolution equations for off-forward parton distributions in leading and next-to-leading orders based on partial conformal wave expansion and orthogonal polynomials reconstruction.
First order phase transitions (FOPTs) are usually described by the nucleation and expansion of new phase bubbles in the old phase background. While the dynamics of new phase bubbles have been extensively studied, a comprehensive treatment…
In this article we propose feature graph architectures (FGA), which are deep learning systems employing a structured initialisation and training method based on a feature graph which facilitates improved generalisation performance compared…
Fractional occupation numbers can be used in density functional theory to create a symmetric Kohn-Sham potential, resulting in orbitals with degenerate eigenvalues. We develop the corresponding perturbation theory and apply it to a system…
A neural network with fixed topology can be regarded as a parametrization of functions, which decides on the correlations between functional variations when parameters are adapted. We propose an analysis, based on a differential geometry…
The fluctuation-dissipation theorem (FDT) is a simple yet powerful consequence of the first-order differential equation governing the dynamics of systems subject simultaneously to dissipative and stochastic forces. The linear learning…
We explore the relationship between the nonlinear matter power spectrum and the various Lagrangian and Standard Perturbation Theories (LPT and SPT). We first look at it in the context of one dimensional (1-d) dynamics, where 1LPT is exact…
We construct the complete set of orders of growth and we define on it the generalized entropy of a dynamical systems. With this object we provide a framework where we can study the separation of orbits of a map beyond the scope of…
We present a general framework for studying harmonic analysis of functions in the settings of various emerging problems in the theory of diffusion geometry. The starting point of the now classical diffusion geometry approach is the…
The stability of functional differential equations under delayed feedback is investigated near a Hopf bifurcation. Necessary and sufficient conditions are derived for the stability of the equilibrium solution using averaging theory. The…
Evolution equations of YFS and DGLAP types in leading order are considered. They are compared in terms of mathematical properties and solutions. In particular, it is discussed how the properties of evolution kernels affect solutions.…
The Jacobi evolution method has been widely used in the QCD analysis of structure function data. However a recent paper claims that there are serious problems with its convergence and stability. Here we briefly review the evidence for the…
We review the present status of polarized structure functions measured in deep-inelastic scattering. We discuss the x and Q^2 dependence of the structure function g_1, and how it can be used to test perturbative QCD at next-to-leading order…
The resummation of $O(\alpha^{l+1} \ln^{2l} x)$ terms in the evolution kernels of non--singlet combinations of structure functions is investigated for both QED abd QCD. Numerical results are presented for unpolarized and polarized structure…
This is the introductory part of my PhD thesis which consists of two parts, the separate introduction and four published articles. The introduction begins by a technically detailed description of the DGLAP evolution and the fast numerical…
We compare standard perturbation theory with the polaron transformation for non-linear transport of electrons through a two-level system. For weak electron-phonon coupling and large bias, there is good agreement between both approaches.…
We prove that the Hopf algebra of parking functions and the Hopf algebra of ordered forests are isomorphic, using a rigidity theorem for a particular type of bialgebras.
We present a general method for the solution of the renormalization group equations for the non-forward parton distributions on the two-loop level in the flavour singlet channel based on an orthogonal polynomial reconstruction. Using this…
Positional reasoning is the process of ordering unsorted parts contained in a set into a consistent structure. We present Positional Diffusion, a plug-and-play graph formulation with Diffusion Probabilistic Models to address positional…
We develop a theory of higher order structures in compact abelian groups. In the frame of this theory we prove general inverse theorems and regularity lemmas for Gowers's uniformity norms. We put forward an algebraic interpretation of the…